Fluid simulation is an essential technology in many areas of technology. For example, it may be used in engineering where dynamic fluid simulation enables testing, optimization and validation of various designs and constructions, or for educational purposes where dynamic fluid simulation enables virtual experiments and exploration based learning. Other examples include virtual reality training simulators (where dynamic fluid simulation enables realistic behavior of ships, vehicles and other machines and devices, as well as load and cargo, or body fluids in surgery training simulators, etc.), environment illustrations in motion pictures (where fluid simulation enable cost effective and spectacular computer generated visual effects of flooding, splashing, explosions and general representation of water and other fluids in containers, floods, lakes and oceans), and contemporary computer games, where interactive simulation of dynamic fluids enriches game play and enables special effects, such as water splashes and explosions.
In a conventional method for pseudo particle based simulation of dynamic fluids, the motion of the simulated fluid is governed by penalty forces that act to preserve the fluid volume and mass density. In addition, the fluid velocity can be corrected by means of a projection of the velocities of a compressible fluid upon a velocity field of a corresponding incompressible fluid. The penalty force method sets severe restriction on the size of the time step of the time discrete computer simulation, since the time step must be small enough to resolve fluctuations of the fluid that propagate through the fluid with the speed of sound of the fluid. The fluid sound speed is often 10-100 times that of other relevant speed scales of the system.
As will become apparent from the description below, conventional penalty force methods are computationally heavy and inefficient in representing dynamic near incompressible fluids. Furthermore, conventional penalty force methods commonly experience severe stabilization problems.
Therefore, conventional methods use a variety of approaches for dealing with the described stability problem. Such methods may comprise a viscosity or damping force being added to the pressure force. The damping of velocities will stabilize the dynamic fluid simulation for larger pressure forces, and thus allow for simulation of more incompressible fluids. However, very large viscosity forces are needed to substantially stabilize these incompressible fluid simulations. In the limit of very large viscosity forces, these forces will themselves start to contribute instabilities to the simulation, and in addition such large viscosity forces will also give highly unrealistic simulations of even the most ordinary well known fluids that have relatively low internal viscosity.
Thus, the overall effect on the dynamic fluid simulation of a very large viscosity is a slightly more stable simulation, a fluid with a still unrealistic degree of compressibility, and a fluid with too much internal viscosity to be realistic.